A modification of the Dewilde-van der Veen method for inversion of finite structured matrices

作     者：Eidelman, Y Gohberg, I 

作者机构：Tel Aviv Univ Raymond & Beverly Sackler Fac Exact Sci Sch Math Sci IL-69978 Tel Aviv Israel 

出 版 物：《LINEAR ALGEBRA AND ITS APPLICATIONS》 (线性代数及其应用)

年 卷 期：2002年第343卷

页      面：419-450页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Israel Academy of Sciences and Humanities Israel Science Foundation, ISF 

主　　题：structured matrices linear complexity algorithms inversion algorithms factorization algorithms solution of linear equations 

摘      要：We study a class of block structured matrices R = {R-ij}(i,j=1)(N) with a property that the solution of the corresponding system Rx = y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference, The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments. (C) 2002 Elsevier Science Inc. All rights reserved.